Question: Maureen rented a lemonade stand for $\$10.00$ per week. She sells her lemonade for $75$ cents per cup, but also spends $25$ cents per cup of lemonade on supplies. How many cups of lemonade must she sell in one week so that her costs (rent and supplies) are equal to her sales?
Let $c$ be the number of cups of lemonade Maureen must sell to break even. Then the expression for the number of cents Maureen spends on her lemonade stand is $1000+25c$, and the expression for the number of cents Maureen earns from her lemonade stand is $75c$. To find the number of cups of lemonade she must sell so that her costs are equal to her sales, we set these two expressions equal and solve for $c$: \begin{align*}1000+25c&=75c \\ 50c&=1000 \\ {c}&=20.\end{align*} Therefore, Maureen must sell $\boxed{20}$ cups of lemonade to break even.